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Tests de modèles non linéaires. (French) Zbl 0572.62071

Alternative approaches to time series analysis, Proc. 3rd Fr.-Belg. Meet. Stat., Rouen/France 1982, Trav. Rech. 1, 45-65 (1984).
[For the entire collection see Zbl 0564.00023.]
From the example of two nonlinear models, \(X(t)=\epsilon (t)+\delta \epsilon (t-1)\epsilon (t-2)\) and \(X(t)=\epsilon (t)+\gamma \epsilon (t- 1)X(t-2),\) \(\epsilon\) (t) being a Gaussian white noise, we show how we can extend Bartlett’s and Quenouille’s tests for choosing between these two models. We estimate consistently the parameters of the two models and with the help of two statistics whose laws are asymptotically known under the null and alternative hypothesis, we construct two tests, whose power is calculated for some values of the parameters.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)

Citations:

Zbl 0564.00023